What does normal focal length really mean?

Question

First off, I wanna say that I have a qualification in photo-/videography and of course I do know the principles of normal focal length, how the angle of view relates with the focal length and sensor/film size. There is this widespread rule that a focal length that is equal or close to the diagonal of the sensor/film dimensions gives a natural field of view or "as the human eye sees". From the first time I heard this I had this sceptical voice inside but I didn't payed much attention until recently.

I took my fullframe sony and the 28-70mm kit lens and turned the zoom until what my eye saw and what I saw through the viewfinder was identical to my perception. The result was somewhere around 68mm. That gives me a diagonal angle of view of ~35 degrees, as opposed to the ~53 degrees for a normal focal length.

Do I have wierd eyes or a misconception about normal focal length?

Answer 1

The original phrase was "normal angle". The earliest reference related to photography that I could find dates to 1909. Earlier references are mostly related to medicine. One photographic reference to a "normal lens" in 1893 was referring to an unmodified lens.

When the focal length is equal to the diagonal of the frame, the angle of view (of the diagonal) is ~53.4 degrees. The angle of view of a 50mm lens on 135 film is ~46.8 degrees.

Whether the image seen in the viewfinder matches that of the photographer's eye depends on the magnification of the viewfinder.

• Points in Focus: Depth of Field (DoF), Angle of View, and Equivalent Lens Calculator

• Complete Self-instructing Library of Practical Photography: Negative retouching, etching and modeling
  James Boniface Schriever
  American School of Art and Photography, 1909

  

Answer 2

Do I have weird eyes or a misconception about normal focal length?

You have a misconception about what "normal focal length" is. But don't feel bad. Your misconception has been oft repeated by many others who claim to be authorities on the subject. They mix up two different concepts: perspective and apparent magnification.

Perspective

A normal lens is one that makes an image created with that focal length combined with an image format using a similarly measured diagonal look "natural" to a human observer. There are several factors involved that have to do with the differences between how a camera records an image of a scene and how the human eye/brain system perceives a scene.

• Accommodation: Although the human eye has a nominal focal length of about 17mm, it can vary with accommodation up to a maximum of 15 diopters!
• Binocular Vision Human vision is binocular. It uses two eyes spaced apart to obtain two slightly different perspectives of a scene. Cameras are typically monocular and only record a single perspective.
• Curved retina The human retina is curved. Film planes and camera sensors are typically flat. The debate has raged for centuries over whether straight lines in the world are perceived as straight or curved by our eyes and whether they should be depicted as straight in a flat picture plane when Abraham Bosse postulated in 1665 that "... one can neither define nor paint as the eye sees."
• Variable Sensitivity There are significant differences in sensitivity between our greater than 180° peripheral vision and the roughly 2° field of view of our foveal vision.
• Cortex Processing The human brain uses its cortex to process the information it receives from both eyes as the scene may change over time to construct an internal model of a scene that is very different from the way a camera records all of the light from a scene falling on a single lens equally for a specific time interval.

Typically, an image produced using a normal lens should be viewed from a distance of around 10-12 inches (25-30 centimeters) to look "natural" to our eyes. We can also get "natural" perspectives by viewing images taken with a wide angle lens at closer distances and images taken with narrow angle lenses (telephoto) at longer distances.

Apparent Magnification

I took my full frame Sony and the 28-70mm kit lens and turned the zoom until what my eye saw and what I saw through the viewfinder was identical to my perception. The result was somewhere around 68mm. That gives me a diagonal angle of view of ~35 degrees, as opposed to the ~53 degrees for a normal focal length.

This is a different issue than that of perspective addressed by the concept of a "normal" lens giving a "natural" perspective. Regarding what you see through a viewfinder compared to what you see with your naked eye, it's all about apparent magnification.

First let's discuss what apparent magnification is: Most simply put it is the size objects look to our eyes when viewed through a lens system compared to how big they look when viewed without that lens system. If I look through a camera viewfinder with my right eye and leave my left eye open I will see an object in front of me with both eyes. If the apparent sizes are the same for both eyes, we would say the lens system (consisting of the total combination of elements in the camera lens as well as the mirror, viewscreen/focusing screen, prism, and eyepiece elements in the viewfinder) to be a magnification of 1X. If the object looks twice as large with my right eye, we would say the magnification is 2X. If the object looks half as large as seen with the right eye via the viewfinder then we would say the magnification is 0.5X.

Now let's discuss the viewfinders in typical SLR cameras. How large something appears when viewed in a camera's eyepiece depends on two factors:

• The focal length of the lens. This affects the size of objects as they are projected on the camera's focusing screen (sometimes also called a viewscreen) as well as projected on the camera's imaging medium. Since the mirrors in every SLR I have ever seen are flat, they provide no magnification as they flip the image up onto the focusing screen. The same is true of the pentaprism or pentamirror in the viewfinder. Since all of the reflecting surfaces are flat they provide no magnification.
• The magnification of the eyepiece. The lenses in a camera's eyepiece are very much like the lenses in a telescope or binocular eyepiece. They provide a magnification, usually a fractional one (that is they make things smaller), and project collimated light through the exit pupil. Our eyes then focus on this collimated light to view the image through the eyepiece. The size of the cylinder (or rectangle) of collimated light projected by the eyepiece is called the exit pupil size.

Many, if not most, 35mm SLR cameras during the second half of the 20th century had viewfinders that provided magnification similar to each other. With a 55-60mm lens attached the apparent magnification was about 1X.¹ That means what we saw through the viewfinder with our right eye was approximately the same size as what we saw with our unaided left eye looking directly at the same scene.

_{¹ The following cameras listed with their viewfinder magnifications with a 50mm lens focused at infinity: Canon F1 - 0.8X, Nikon F - 0.8X, Canon AE-1 - 0.86X, Minolta X-570 - 0.9X, Pentax K2 - 0.88X, Pentax ME-F - 0.87X. A 0.9X viewfinder would give 1X apparent magnification at roughly 55mm, a 0.8X viewfinder would do so at roughly 62mm.}

In the digital age that standardization has been severely altered. Cameras have a wide variety of sensor sizes. Viewfinder sizes vary more from camera to camera. In the manual focus only portion (which was most) of the film era even lower priced cameras needed large, bright viewfinders to enable their users to focus them properly. With the advent of autofocus large bright viewfinders have become more of a luxury than a necessity and are seen mostly on the more expensive models. Differences in sensor sizes affect how much magnification is needed for the viewfinder to display approximately the same field of view as the FoV the imaging sensor will capture.

Here are a couple of examples:

• Compare the EOS REbel XTi/400D to the EOS 7D. Both have the same sized sensor: an APS-C sensor measuring approximately 22.2x14.8mm. The viewfinder on the entry level Rebel shows 95% of the sensor coverage at a magnification of 0.80X. The viewfinder on the 7D shows 100% of the sensor coverage at a magnification of 1.0X. Thus when a user looks in the two viewfinders from the same eye relief (distance behind the exit pupil), the image in the viewfinder of the Rebel XTi looks about 3/4 as large (0.76) as the image seen in the viewfinder of the 7D. If the same focal length lens is mounted on both cameras, the apparent magnification of items in the scene would be about 4/3 more (1.316) with the 7D than with the Rebel XTi.

• Compare the EOS 1Ds Mark II and the EOS 1Ds Mark III. They both had identically sized 36x24mm FF sensors. Both viewfinders provided 100% coverage. The 1Ds Mark III had a larger viewfinder with a 0.76X magnification compared to the 1Ds Mark II with a 0.70X magnification. With the same lens mounted on each they both provided the same FoV. But the larger viewfinder made the same FoV appear 8.6% larger. This can be compared to viewing a 25" television next to a 23" television with identical resolutions. Both are showing the same information, but each item in the picture is 8.6% larger on the 25" screen.

Now let's compare modern digital cameras to the old SLR standards.¹ Remember that viewfinder magnification specs are measured with a 50mm lens focused at infinity. Canon's three most recent 1-Series FF cameras have viewfinder magnifications of 0.76X. That translates to about a 65mm lens need to get apparent 1X magnification through the viewfinder. All of Canon's other FF digital cameras (the 5-series and the 6D) have viewfinder magnifications of 0.71X which translates to roughly a 70mm lens needed for 1X apparent magnification.

Canon's recent APS-C models range from 0.8X for the Rebel T5/1200D to 1.0X for the 7D Mark II. That leaves quite a bit of range for apparent 1X magnification: Anywhere from 50mm for the 7D2 to 62mm for the 1200D. See how the rule of thumb is disappearing with the various differences between camera models? We need anywhere from a 50mm to a 70mm lens to get the same apparent magnification looking through the viewfinders of various EOS DSLRs.

Keep in mind that the FoV with an APS-C camera will be much smaller than the FoV of a FF camera if both have the same magnification. In fact, the total apparent width of the view in the 1.0X 7D2 viewfinder is not as wide as the 0.76X viewfinder of the 1D X or even of the 0.71X 5D3. That is because the APS-C sensor/mirror/viewscreen size is only about 0.63X as wide as the FF sensor/mirror/viewscreen. So now the waters are even muddier!

By now it should be apparent that only when you have a specific camera model in mind can you compare the magnification of an unaided human eye with the apparent magnification observed when looking through the viewfinder of a camera with a lens of a particular focal length.

Answer 3

First: The rule-of-thumb: “Human perspective is achieved when the focal length about matches the diagonal measure of the format”. This lash-up yields a diagonal angle of view of about 53⁰. A still camera, such as a 35mm with an aspect ratio of 1:1.5, will deliver a 45⁰ horizontal angle of view. Such a lash-up is labeled “normal”. Historically, focal length matching diagonal measure is not likely to display a vignette.

When most people say “identical to my perception”, usually they have one eye peering through the viewfinder and the other unaided. They then adjust the zoom until the two images match as to magnification. My Nikon F matches at 58mm. This is important when on the sidelines shooting football; if your camera view is reality, this gives you time to get out of the way (object seen in side mirror are smaller than reality).

The real facts, if you take a picture and make a print and view it from normal reading distance (250mm), the image on paper will likely display a proper perspective. For most images this obscure fact is of no importance. “Normal” is focal length about equal to diagonal measure. Wide angle is about 70% of this value or shorter. Telephoto is about twice “normal” or longer. Portrait lens is about 2 ½ time “normal”.

However art follows the rules of your heart, not science.